Survival of the Aligned: Ordering of the Plant Cortical Microtubule Array

The cortical array is a structure consisting of highly aligned microtubules which plays a crucial role in the characteristic uniaxial expansion of all growing plant cells. Recent experiments have shown polymerization-driven collisions between the membrane-bound cortical microtubules, suggesting a possible mechanism for their alignment. We present both a coarse-grained theoretical model and stochastic particle-based simulations of this mechanism, and we compare the results from these complementary approaches. Our results indicate that collisions that induce depolymerization are sufficient to generate the alignment of microtubules in the cortical array.

Figure 1

Transverse cortical array in an etiolated dark-grown Arabidopsis thaliana hypocotyl cell with fluorescently labeled microtubules. Image courtesy of Jelmer Lindeboom, Wageningen University.

Figure 2

(a) Schematic overview of the included effects and parameters in the model. (b) Relative frequency of collision outcomes as a function of angle of incidence used in our model.

Figure 3

Comparison between theoretical (solid lines) and simulation results (symbols). The simulations were performed on a $80\mu m\times 80\mu \mathrm{m}$ system with periodic boundary conditions. The spontaneous catastrophe rate was varied to probe different values of $G$: $r_c\in [4\times {10}^{-3},1.2\times {10}^{-2}]{\mathrm{s}}^{-1}$. The nucleation rate was set to $r_n=0.003\mu {\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$ and other parameters were taken from [4] (interphase BY-2 cells): $v^{+}=0.078\mu \mathrm{m}{\mathrm{s}}^{-1}$, $v^{-}=0.164\mu \mathrm{m}{\mathrm{s}}^{-1}$, and $r_r=6.8\times {10}^{-3}{\mathrm{s}}^{-1}$. Measurements were performed after equilibrating for 50 000 s (a) or 250 000 s (b); $G$ was increased between measurements. The standard error of the mean is typically smaller than the symbols and is otherwise indicated by vertical bars. $N=80$ (a), 40 (b).